Abstract:We introduce a variant of the Localization game in which the cops only have visibility one, along with the corresponding optimization parameter, the onevisibility localization number ζ1. By developing lower bounds using isoperimetric inequalities, we give upper and lower bounds for ζ1 on k-ary trees with k ≥ 2 that differ by a multiplicative constant, showing that the parameter is unbounded on kary trees. We provide a O( √ n) bound for K h -minor free graphs of order n, and we show Cartesian grids meet this bo… Show more
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